VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

【摘要】 Let H₁, H₂, H₃ be real Hilbert spaces, let A : H₁→ H₃, B : H₂→ H₃ be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H₁→ H₁ and T : H₂→ H₂ are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H₁: Ux = x} and F（T） = {x ∈ H₂: Tx = x}. Note that,by taking B = I and H₂= H₃ in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.更多还原

【Abstract】 Let H₁, H₂, H₃ be real Hilbert spaces, let A : H₁→ H₃, B : H₂→ H₃ be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H₁→ H₁ and T : H₂→ H₂ are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H₁: Ux = x} and F（T） = {x ∈ H₂: Tx = x}. Note that,by taking B = I and H₂= H₃ in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.更多还原